Module DR (by Aaron Pixton)¶
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admcycles.DR.betti(g, r, marked_points=(), moduli_type=3)[source]¶ This function returns the predicted rank of the codimension r grading of the tautological ring of the moduli space of stable genus g curves with marked points labeled by the multiset marked_points.
g and r should be nonnegative integers and marked_points should be a tuple of positive integers.
The parameter moduli_type determines which moduli space to use: - MODULI_ST: all stable curves (this is the default) - MODULI_CT: curves of compact type - MODULI_RT: curves with rational tails - MODULI_SM: smooth curves
EXAMPLES:
sage: from admcycles.DR import betti
Check rank R^3(bar{M}_2) = 1:
sage: betti(2,3) 1
Check rank R^2(bar{M}_{2,3}) = 44:
sage: betti(2,2,(1,2,3)) 44
Check rank R^2(bar{M}_{2,3})^{S_3} = 20:
sage: betti(2,2,(1,1,1)) 20
Check rank R^2(bar{M}_{2,3})^{S_2} = 32 (S_2 interchanging markings 1 and 2):
sage: betti(2,2,(1,1,2)) 32
Check rank R^2(M^c_4) = rank R^3(M^c_4) = 6:
sage: from admcycles.DR import MODULI_CT, MODULI_RT, MODULI_SM sage: betti(4,2,(),MODULI_CT) 6 sage: betti(4,3,(),MODULI_CT) 6
Check rank R^8(M^rt_{17,2})^(S_2) < R^9(M^rt_{17,2})^(S_2):
sage: betti(17,8,(1,1),MODULI_RT) # long time 122 sage: betti(17,9,(1,1),MODULI_RT) # long time 123
Check rank R^9(M_{20,1}) < rank R^10(M_{20,1}):
sage: betti(20,9,(1,),MODULI_SM) # long time 75 sage: betti(20,10,(1,),MODULI_SM) # long time 76
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admcycles.DR.gorenstein(g, r, marked_points=(), moduli_type=3)[source]¶ This function returns the rank of the codimension r grading of the Gorenstein quotient of the tautological ring of the moduli space of genus g curves with marked points labeled by the multiset marked_points.
g and r should be nonnegative integers and marked_points should be a tuple of positive integers.
The parameter moduli_type determines which moduli space to use: - MODULI_ST: all stable curves (this is the default) - MODULI_CT: curves of compact type - MODULI_RT: curves with rational tails
EXAMPLES:
sage: from admcycles.DR import gorenstein
Check rank Gor^3(bar{M}_{3}) = 10:
sage: gorenstein(3,3) 10
Check rank Gor^2(bar{M}_{2,2}) = 14:
sage: gorenstein(2,2,(1,2)) 14
Check rank Gor^2(bar{M}_{2,2})^{S_2} = 11:
sage: gorenstein(2,2,(1,1)) 11
Check rank Gor^2(M^c_{4}) = 6:
sage: from admcycles.DR import MODULI_CT, MODULI_RT sage: gorenstein(4,2,(),MODULI_CT) 6
Check rank Gor^4(M^rt_{8,2}) = 22:
sage: gorenstein(8,4,(1,2),MODULI_RT) 22